Simplify the following expression: $x = \dfrac{-4n^2 + 48n - 80}{n - 2} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-4$ , so we can rewrite the expression: $ x =\dfrac{-4(n^2 - 12n + 20)}{n - 2} $ Then we factor the remaining polynomial: $n^2 {-12}n + {20} $ ${-2} {-10} = {-12}$ ${-2} \times {-10} = {20}$ $ (n {-2}) (n {-10}) $ This gives us a factored expression: $\dfrac{-4(n {-2}) (n {-10})}{n - 2}$ We can divide the numerator and denominator by $(n + 2)$ on condition that $n \neq 2$ Therefore $x = -4(n - 10); n \neq 2$